Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models

Abstract

In silico experiments bear the potential for further understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results. Cell polarization and spatial reorganization of membrane proteins are fundamental for cell division, chemotaxis and morphogenesis. We chose the yeast Saccharomyces cerevisiae as an exemplary model system which entails the shuttling of small Rho GTPases such as Cdc42 and Rho, between an active membrane-bound form and an inactive cytosolic form. We used partial differential equations to describe the membrane-cytosol shuttling of proteins. In this study, a consistent extension of a class of 1D reaction-diffusion systems into higher space dimensions is suggested. The membrane is modeled as a thin layer to allow for lateral diffusion and the cytosol is modeled as an enclosed volume. Two well-known polarization mechanisms were considered. One shows the classical Turing-instability patterns, the other exhibits wave-pinning dynamics. For both models, we investigated how cell shape and diffusion barriers like septin structures or bud scars influence the formation of signaling molecule clusters and subsequent polarization. An extensive set of in silico experiments with different modeling hypotheses illustrated the dependence of cell polarization models on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. In particular, the results of our computer simulations suggested that for both mechanisms, local diffusion barriers on the membrane facilitate Rho GTPase aggregation, while diffusion barriers in the cytosol and cell protrusions limit spontaneous molecule aggregations of active Rho GTPase locally.

A coupled bulk-surface model for cell polarisation

“…We remark that I(b) is an increasing function, since is an increasing function, by continuity it follows that I(b 1 + ε) < 0 and I(b 2 − ε) > 0. This shows the existence of the critical value b c and for (19) we know that for b > b c then a increases its high concentration region.…”

Mechanisms of cell polarization

“…A recent work describes the formation of special cell appendages, regulated by a balance of Rac Arp2/3 pathway (promotes the formation of “fin-like” structures) and Rho pathways that promote formin-based actin assembly and myosin-based blebbing behavior [141]. Several modeling studies have explored the connections between the shape of a cell and the dynamics of its intracellular signaling for polarity [5,97,142–144], but these have largely focused on 2D cell projections. The computational issues associated with simulating dynamic intracellular signaling inside a deforming 3D cell are still daunting, but developments of new methods is ongoing by several groups (see, e.g.…”

Osmolyte homeostasis controls single-cell growth rate and maximum cell size ofSaccharomyces cerevisiae

“…To describe this coordinated growth, two instances of the SCGM with different initial volumes were coupled by allowing water and osmolyte fluxes between the instances. For simplicity, we neglected the specific bud localization at the mother, which would include the complex polarization process (42,43). This coupled SCGM can be interpreted as an augmented model compared to a previous de-scription of interconnected soap bubbles or balloons (30,44).…”